Simplify the following expression: $ x = \dfrac{7}{6} - \dfrac{-6k}{-5k - 2} $
In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{-5k - 2}{-5k - 2}$ $ \dfrac{7}{6} \times \dfrac{-5k - 2}{-5k - 2} = \dfrac{-35k - 14}{-30k - 12} $ Multiply the second expression by $\dfrac{6}{6}$ $ \dfrac{-6k}{-5k - 2} \times \dfrac{6}{6} = \dfrac{-36k}{-30k - 12} $ Therefore $ x = \dfrac{-35k - 14}{-30k - 12} - \dfrac{-36k}{-30k - 12} $ Now the expressions have the same denominator we can simply subtract the numerators: $x = \dfrac{-35k - 14 + 36k }{-30k - 12} $ Distribute the negative sign: $x = \dfrac{-35k - 14 + 36k}{-30k - 12}$ $x = \dfrac{k - 14}{-30k - 12}$ Simplify the expression by dividing the numerator and denominator by -1: $x = \dfrac{-k + 14}{30k + 12}$